Logarithmic Relation of Entropy and Symmetry

The relations of the two most important concepts, entropy and symmetry, are
mathematically clarified. It has been a tacit assumption that higher symmetry
of a system imply less entropy. However, it is proved here that the opposite is
true for both dynamic and static systems. Higher value of entropy of any system
is correlated to higher symmetry. Entropy (S) of a system of w
microstates is expressed as a logarithmic function of symmetry,

The apparent symmetry number is

where
is the probability of the ith microstate.

This relation is broadly useful for solving problems of relative structural
stability of both dynamic systems and static structures [1-4].

[3] (a) S.-K. Lin, Understanding structural stability and process
spontaneity based on the rejection of the Gibbs paradox of entropy of
mixing. Paper presented at the Fourth World Congress of Theoretically
Oriented Chemists, Jerusalem, Israel, July 7-12, 1996.